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A Graphical Analysis of Some Basic Results in Social Choice

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Estelle Cantillon

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Abstract

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0268.

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Date of creation: Mar 2001
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Handle: RePEc:nbr:nberte:0268

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Find related papers by JEL classification:
H0 - Public Economics - - General
D7 - Microeconomics - - Analysis of Collective Decision-Making

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  1. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December. [Downloadable!] (restricted)
  2. Blackorby, C. & Donaldson, D. & Weymark, J.A., 1990. "A Welfarist Proof Of Arrow'S Theorem," UBC Departmental Archives 90-16, UBC Department of Economics.
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  3. Saari, Donald G., 1991. "Calculus and extensions of Arrow's theorem," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 271-306. [Downloadable!] (restricted)
  4. Balasko, Yves & Cres, Herve, 1997. "The Probability of Condorcet Cycles and Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 237-270, August. [Downloadable!] (restricted)
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